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50 Videos

Determine whether each relation is a function, and state its domain and range.

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Q1a

Determine whether each relation is a function, and state its domain and range.

```
\displaystyle
3x^2 + 2y =6
```

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Q1b

Determine whether each relation is a function, and state its domain and range.

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Q1c

Determine whether each relation is a function, and state its domain and range.

```
\displaystyle
x = 2^y
```

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Q1d

A cell phone company charges a monthly fee of $30, plus $0.02 per minute of call time.

a) Write the monthly cost function, `C(t)`

, where t is the amount of time in minutes of call time during a month.

b) Find the domain and range of `C`

.

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Q2

Graph `f(x) = 2|x + 3| -1`

, and state the domain and range.

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Q3

Describe this interval using absolute value notation.

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Q4

For the pair of functions, give a characteristic that the two functions have in common and a characteristic that distinguishes them.

```
\displaystyle
f(x) =x^2
```

and ```
\displaystyle
g(x) = \sin x
```

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Q5a

For the pair of functions, give a characteristic that the two functions have in common and a characteristic that distinguishes them.

```
\displaystyle
f(x) =\frac{1}{x}
```

and ```
\displaystyle
g(x) = x
```

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Q5b

For the pair of functions, give a characteristic that the two functions have in common and a characteristic that distinguishes them.

```
\displaystyle
f(x) =x^2
```

and ```
\displaystyle
g(x) = \sin x
```

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Q5c

```
\displaystyle
f(x) =2^x
```

and ```
\displaystyle
g(x) = x
```

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Q5d

Identify the intervals of increase/decrease, the symmetry, and the domain and rage of each function.

```
\displaystyle
f(x) = 3x
```

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Q6a

Identify the intervals of increase/decrease, the symmetry, and the domain and range of each function.

```
\displaystyle
f(x) = x^2+ 2
```

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Q6b

For each of the following equations, state the parent function and the transformations that were applied. Graph the transformed function.

```
\displaystyle
f(x) =|x + 1|
```

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Q7a

For each of the following equations, state the parent function and the transformations that were applied. Graph the transformed function.

```
\displaystyle
f(x) = -0.25\sqrt{3(x+ 7)}
```

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Q7b

For each of the following equations, state the parent function and the transformations that were applied. Graph the transformed function.

```
\displaystyle
f(x) = -2\sin(3x) + 1, 0 \leq x \leq 360^o
```

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Q7c

```
\displaystyle
f(x) = 2^{-2x} -3
```

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Q7d

The graph of `y = x^2`

is horizontally stretched by a factor of 2, reflected in the x—axis, and shifted 3 units down. Find the equation that results from the transformation, and graph it.

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Q8

`(2, 1)`

is a point on the graph of `y =f(x)`

. Find the corresponding point on the graph of each of the following functions.

```
\displaystyle
y = -f(-x)+2
```

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Q9a

`(2, 1)`

is a point on the graph of `y =f(x)`

. Find the corresponding point on the graph of each of the following functions.

```
\displaystyle
y =f(-2(x+ 9)) - 7
```

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Q9b

`(2, 1)`

is a point on the graph of `y =f(x)`

. Find the corresponding point on the graph of each of the following functions.

```
\displaystyle
y =f(x -2) + 2
```

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Q9c

`(2, 1)`

is a point on the graph of `y =f(x)`

. Find the corresponding point on the graph of each of the following functions.

```
\displaystyle
y = 0.3f(5(x-3))
```

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Q9d

`(2, 1)`

is a point on the graph of `y =f(x)`

. Find the corresponding point on the graph of each of the following functions.

```
\displaystyle
y = 1 -f(1-x)
```

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Q9e

`(2, 1)`

is a point on the graph of `y =f(x)`

. Find the corresponding point on the graph of each of the following functions.

```
\displaystyle
y = -f(2(x - 8))
```

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Q9f

For the point on a function, state the corresponding point on the inverse relation.

(1, 2)

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Q10a

For the point on a function, state the corresponding point on the inverse relation.

(-1, -9)

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Q10b

For the point on a function, state the corresponding point on the inverse relation.

(0, 7)

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Q10c

For the point on a function, state the corresponding point on the inverse relation.

f(5) = 7

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Q10d

For the point on a function, state the corresponding point on the inverse relation.

g(0) = -3

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Q10e

For the point on a function, state the corresponding point on the inverse relation.

`h(1) = 10`

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Q10f

Given the domain and range of a function, state the domain and range of the inverse relation.

`D = \{x\in \mathbb{R}\}`

, ```
\displaystyle
R = \{y \in \mathbb{R}, -2 < y < 2\}
```

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Q11a

Given the domain and range of a function, state the domain and range of the inverse relation.

`D = \{x\in \mathbb{R}, x \geq 7\}`

, ```
\displaystyle
R = \{y \in \mathbb{R}, y < 12\}
```

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Q11b

Graph the function and its inverse relation on the same set of axes. Determine whether the inverse relation is a function.

`f(x) = x^2 -4`

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Q12a

Graph the function and its inverse relation on the same set of axes. Determine whether the inverse relation is a function.

`f(x) = 2^x`

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Q12b

Find the inverse of each function.

`f(x) = 2x + 1`

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Q13a

Find the inverse of each function.

`f(x) = x^3`

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Q13b

Graph the following function. Determine whether it is discontinuous and, if so, where. State the domain and the range of the function.

```
\displaystyle
f(x) =
\begin{cases}
&2x, &\text{when } x < 1 \\
&x +1, &\text{when } x \geq 1
\end{cases}
```

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Q14

Write the algebraic representation for the following piecewise function, using function notation.

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Q15

If

```
\displaystyle
f(x) =
\begin{cases}
&x^2 +1, &\text{when } x < 1 \\
&3x, &\text{when } x \geq 1
\end{cases}
```

is `f(x)`

continuous at `x =1`

? Explain.

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Q16

A telephone company charges $30 a month and gives the customer 200 free call minutes. After the 200 min, the company charges $0.03 a minute.

a) Write the function using function notation.

b) Find the cost for talking 350 min in a month.

c) Find the cost for talking 180 min in a month.

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Q17

Given `f = \{(0, 6), (1, 3), (4, 7), (5, 8)\}`

and `g= \{(-1, 2), (1, 5), (2, 3) ,(4, 8), (8, 9)\}`

, determine

`f(x) + g(x)`

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Q18a

Given `f = \{(0, 6), (1, 3), (4, 7), (5, 8)\}`

and `g= \{(-1, 2), (1, 5), (2, 3) ,(4, 8), (8, 9)\}`

, determine

`f(x)- g(x)`

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Q18b

Given `f = \{(0, 6), (1, 3), (4, 7), (5, 8)\}`

and `g= \{(-1, 2), (1, 5), (2, 3) ,(4, 8), (8, 9)\}`

, determine

`f(x)\cdot g(x)`

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Q18c

Given `f(x) = 2x^2 -2x, -2 \leq x \leq 3`

and `g(x) = -4x, -3 \leq x \leq 5`

, graph the following.

`f`

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Q19a

Given `f(x) = 2x^2 -2x, -2 \leq x \leq 3`

and `g(x) = -4x, -3 \leq x \leq 5`

, graph the following.

`g`

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Q19b

Given `f(x) = 2x^2 -2x, -2 \leq x \leq 3`

and `g(x) = -4x, -3 \leq x \leq 5`

, graph the following.

`f +g`

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Q19c

Given `f(x) = 2x^2 -2x, -2 \leq x \leq 3`

and `g(x) = -4x, -3 \leq x \leq 5`

, graph the following.

`f -g`

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Q19d

Given `f(x) = 2x^2 -2x, -2 \leq x \leq 3`

and `g(x) = -4x, -3 \leq x \leq 5`

, graph the following.

`fg`

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Q19e

`f(x) = x^2 +2x`

and `g(x) = x + 1`

. Match the answer with the operation.

```
\displaystyle
\begin{array}{llllllll}
&(a) \phantom{.} x^3 + 3x^2 + 2x
&A \phantom{.} f(x) + g(x) \\
&(b) \phantom{.} -x^2 -x + 1
&A \phantom{.} f(x) - g(x) \\
&(c) \phantom{.} x^2 +3x + 1
&A \phantom{.} g(x) - f(x) \\
&(d) \phantom{.} x^2 +x - 1
&A \phantom{.} g(x) \times f(x)
\end{array}
```

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Q20

`f(x) = x^3 +2x^2`

and `g(x) = -x + 6`

.

a) Complete the table.

b) Use the table to graph `f(x)`

and `g(x)`

on the same axes.

c) Graph (f 1 g)(x) on the same axes as part b).

d) State the equation of `(f + g)(x)`

.

e) Verify the equation of `(f + g)(x)`

using two of the ordered pairs in the table.

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Q21